Saturated fusion systems with parabolic families

Details Saturated fusion systems with parabolic families Saturated fusion systems with parabolic families

2010-08-23

arxiv.org/abs/1008.3815v2

Mathematics

Group Theory

28 pages

Scientific paper

Let G be group; a finite p-subgroup S of G is a Sylow p-subgroup if every finite p-subgroup of G is conjugate to a subgroup of S. In this paper, we examine the relations between the fusion system over S which is given by conjugation in G and a certain chamber system C, on which G acts chamber transitively with chamber stabilizer N_G(S). Next, we introduce the notion of a fusion system with a parabolic family and we show that a chamber system can be associated to such a fusion system. We determine some conditions the chamber system has to fulfill in order to assure the saturation of the underlying fusion system. We give an application to fusion systems with parabolic families of classical type.

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